Data structures for retrieval on integer grids

A family of data structures is presented for retrieval of the sum of values of points within a half-plane or polygon, given that the points are on integer coordinates in the plane. Fredman has shown that the problem has a lower bound of Ω(N^2/3) for intermixed updates and retrievals. Willard has shown an upper bound of O(N^2log6^4) for the case where the points are not restricted to integer coordinates.We have developed families of related data structures for retrievals of half-planes or polygons. One of the data structures permits intermixed updates and half-plane retrievals in O(N^2/3log N) time, where N is the size of the grid.We use a technique we call "Rotation" to permit a better match of a portion of the data structure to the particular problem. Rotations appear to be an effective method for trading-off storage redundancy against retrieval time for certain classes of problems

Insurance and the Limits of Rational Discrimination

As the state of the insurance industry indicates, policy makers and academics have reached little consensus about how to address the implications of rational discrimination. This Current Topic argues that rational discrimination should not be viewed simply as a question of profitability or financial interests, but must also be approached from a moral perspective. Part One examines the underlying cause of rational discrimination in one particular insurance market,\u27 locating its ultimate source in the historical injustices perpetrated against Blacks. This section condemns rational discrimination for perpetuating and even exacerbating social inequalities. The analysis suggests that our society will not fully succeed in reducing economic asymmetries between Blacks and Whites unless it confronts rational, as well as irrational, discrimination. Parts Two and Three examine two alternative methods of interfering with rational discrimination in insurance: prohibiting the practice altogether or compensating for its deleterious effects through a subsidy. While either approach will reduce the correlation between race and risk, this analysis suggests that a subsidy offers significant moral and practical advantages over a prohibition

Facilitating Better Law Teaching – Now

This Essay is about solutions—real solutions that law schools can deploy right now to improve the education we provide. And it is about how to overcome obstacles to implementing those solutions right now. This is how change happens

No Intent, No Foul? Unconscious Bias in Employment Decisions

Many commentators have criticized current anti-discrimination law on the grounds that it does not adequately prohibit unconscious bias in employment decisions. That claim is wrong: Unconscious bias is fully actionable, and it can generally be proved by knowledgeable employment lawyers. The idea behind unconscious bias is that well-meaning employers and supervisors, who would likely consider themselves supporters or even champions of equality, might subconsciously harbor attitudes that result in negative employment decisions for women and minorities

Reconsidering Attraction in Sexual Harassment

This Article will proceed in four parts. Part I explains the significance of the attraction-based view to the law of sexual harassment. This Part demonstrates not only how the attraction-based view provides a theoretical basis for treating workplace sexual conduct as a form of sex discrimination, but also how this view works in practice to provide relief for victims of workplace sexual conduct in a streamlined and effective manner. This Part articulates in a comprehensive manner how an attraction-based paradigm can be used to construct a theory by which plaintiffs can show that workplace sexual conduct has occurred because of\u27 sex ( discriminatory causation or causation ), as required by most anti-discrimination laws. It calls the method of proving discriminatory causation attraction theory. This Part also explains the powerful influence attraction theory has exerted on the development of sexual harassment law. Part II explores the limits of attraction theory. First, this Part explains the essential criticisms offered by power-based theorists. In particular, despite its potential usefulness in many cases, power-based theorists have argued that attraction theory will not work to prove causation (1) in cases involving bisexual harassers (the bisexuality gap ); and (2) in cases where sexual conduct is motivated not by sexual attraction, but rather by something else, such as animosity or a desire to humiliate or exclude the victim (the nonattraction gap ). This Part then explores a practical gap that may result in attraction theory from difficulties in proving attraction and sexual orientation (the conditions necessary for the use of attraction theory). This Part argues that even though these theoretical and practical coverage gaps are real, they are not as large as modem scholars have tended to suppose. Moreover, the practical gap from difficulties in proof could be largely eliminated through the use of a presumption regarding sexual orientation in all attraction-based cases, as opposed to the presumption currently applied by the courts, which only applies to opposite-sex cases. In any event, this Part concludes, none of these gaps are so large as to render attraction theory useless or to justify the abandonment of the theory altogether. Part III examines the normative criticisms that might be leveled at attraction theory. It will conclude that, while attraction theory does pose some normative problems, few of these are insurmountable-and none would appear to justify leaving certain plaintiffs in sexual harassment cases without a remedy, which is what will likely occur if we forego the use of attraction theory. Part IV turns to the power-based theories, concluding that they are riddled with practical limitations and are actually inferior to attraction theory as a vehicle for providing relief. In particular, this Part explains that there are likely to be a set of cases in which attraction theory will work to prove causation but in which a power-based theory will be difficult or will not work. In these cases foregoing the use of attraction theory, as many of the second-generation feminists seem to urge, could easily result in leaving plaintiffs without a remedy

Response to the David Segal article, November 19, 2011, in New York Times

As David Segal’s November 19 article accurately reflects, the legal market is changing. Clients are no longer willing to foot the bill for young lawyers’ training, and thus law firms are increasingly looking to the law schools to produce practice-ready graduates. The good news is that there are clear solutions to the problem, and they are already in motion. A report published in 2007 by the Carnegie Foundation entitled Education Lawyers identified precisely the problem described in Mr. Segal’s article and suggested that law schools should address it by developing courses that educate law students on three levels: knowledge, practice and professional identity. By providing experiential learning opportunities that combine these three values, law schools can produce practice-ready graduates, who are able to provide value to clients the day they leave law school

A Rosetta Stone for Causation

The law of mental causation—or motives—is a mess. It is as if writers in the field are using different languages to describe a multiplicity of causal concepts. The plethora of causal terms and lack of definitional clarity make it difficult to understand the relationship among causal concepts within a single area of law, let alone across substantive areas of law. To reach a clear and consistent understanding of this mess, it would be useful to have a Rosetta Stone—a translation key describing causal concepts and the relationships among those concepts in a precise and universal way. Andrew Verstein’s article, The Jurisprudence of Mixed Motives, comes close to reaching this ideal. However, his model suffers from two critical flaws: failing to justify a key analytical move and using terminology that is more confusing than it is universal. In this Response, I suggest remedies to those problems as well as a way to transform Verstein’s model into a Rosetta Stone for mental causation